%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU267+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 06:29:36 EST 2010
% Result : Theorem 0.25s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 6 unt; 0 def)
% Number of atoms : 122 ( 118 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 158 ( 67 ~; 63 |; 22 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 122 ( 18 sgn 72 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1] :
( ? [X2,X3] : X1 = ordered_pair(X2,X3)
=> ! [X2] :
( X2 = pair_first(X1)
<=> ! [X3,X4] :
( X1 = ordered_pair(X3,X4)
=> X2 = X3 ) ) ),
file('/tmp/tmpmnqcXM/sel_SEU267+1.p_1',d1_mcart_1) ).
fof(2,axiom,
! [X1] :
( ? [X2,X3] : X1 = ordered_pair(X2,X3)
=> ! [X2] :
( X2 = pair_second(X1)
<=> ! [X3,X4] :
( X1 = ordered_pair(X3,X4)
=> X2 = X4 ) ) ),
file('/tmp/tmpmnqcXM/sel_SEU267+1.p_1',d2_mcart_1) ).
fof(18,conjecture,
! [X1,X2] :
( pair_first(ordered_pair(X1,X2)) = X1
& pair_second(ordered_pair(X1,X2)) = X2 ),
file('/tmp/tmpmnqcXM/sel_SEU267+1.p_1',t7_mcart_1) ).
fof(20,negated_conjecture,
~ ! [X1,X2] :
( pair_first(ordered_pair(X1,X2)) = X1
& pair_second(ordered_pair(X1,X2)) = X2 ),
inference(assume_negation,[status(cth)],[18]) ).
fof(24,plain,
! [X1] :
( ! [X2,X3] : X1 != ordered_pair(X2,X3)
| ! [X2] :
( ( X2 != pair_first(X1)
| ! [X3,X4] :
( X1 != ordered_pair(X3,X4)
| X2 = X3 ) )
& ( ? [X3,X4] :
( X1 = ordered_pair(X3,X4)
& X2 != X3 )
| X2 = pair_first(X1) ) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(25,plain,
! [X5] :
( ! [X6,X7] : X5 != ordered_pair(X6,X7)
| ! [X8] :
( ( X8 != pair_first(X5)
| ! [X9,X10] :
( X5 != ordered_pair(X9,X10)
| X8 = X9 ) )
& ( ? [X11,X12] :
( X5 = ordered_pair(X11,X12)
& X8 != X11 )
| X8 = pair_first(X5) ) ) ),
inference(variable_rename,[status(thm)],[24]) ).
fof(26,plain,
! [X5] :
( ! [X6,X7] : X5 != ordered_pair(X6,X7)
| ! [X8] :
( ( X8 != pair_first(X5)
| ! [X9,X10] :
( X5 != ordered_pair(X9,X10)
| X8 = X9 ) )
& ( ( X5 = ordered_pair(esk1_2(X5,X8),esk2_2(X5,X8))
& X8 != esk1_2(X5,X8) )
| X8 = pair_first(X5) ) ) ),
inference(skolemize,[status(esa)],[25]) ).
fof(27,plain,
! [X5,X6,X7,X8,X9,X10] :
( ( ( X5 != ordered_pair(X9,X10)
| X8 = X9
| X8 != pair_first(X5) )
& ( ( X5 = ordered_pair(esk1_2(X5,X8),esk2_2(X5,X8))
& X8 != esk1_2(X5,X8) )
| X8 = pair_first(X5) ) )
| X5 != ordered_pair(X6,X7) ),
inference(shift_quantors,[status(thm)],[26]) ).
fof(28,plain,
! [X5,X6,X7,X8,X9,X10] :
( ( X5 != ordered_pair(X9,X10)
| X8 = X9
| X8 != pair_first(X5)
| X5 != ordered_pair(X6,X7) )
& ( X5 = ordered_pair(esk1_2(X5,X8),esk2_2(X5,X8))
| X8 = pair_first(X5)
| X5 != ordered_pair(X6,X7) )
& ( X8 != esk1_2(X5,X8)
| X8 = pair_first(X5)
| X5 != ordered_pair(X6,X7) ) ),
inference(distribute,[status(thm)],[27]) ).
cnf(31,plain,
( X4 = X5
| X1 != ordered_pair(X2,X3)
| X4 != pair_first(X1)
| X1 != ordered_pair(X5,X6) ),
inference(split_conjunct,[status(thm)],[28]) ).
fof(32,plain,
! [X1] :
( ! [X2,X3] : X1 != ordered_pair(X2,X3)
| ! [X2] :
( ( X2 != pair_second(X1)
| ! [X3,X4] :
( X1 != ordered_pair(X3,X4)
| X2 = X4 ) )
& ( ? [X3,X4] :
( X1 = ordered_pair(X3,X4)
& X2 != X4 )
| X2 = pair_second(X1) ) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(33,plain,
! [X5] :
( ! [X6,X7] : X5 != ordered_pair(X6,X7)
| ! [X8] :
( ( X8 != pair_second(X5)
| ! [X9,X10] :
( X5 != ordered_pair(X9,X10)
| X8 = X10 ) )
& ( ? [X11,X12] :
( X5 = ordered_pair(X11,X12)
& X8 != X12 )
| X8 = pair_second(X5) ) ) ),
inference(variable_rename,[status(thm)],[32]) ).
fof(34,plain,
! [X5] :
( ! [X6,X7] : X5 != ordered_pair(X6,X7)
| ! [X8] :
( ( X8 != pair_second(X5)
| ! [X9,X10] :
( X5 != ordered_pair(X9,X10)
| X8 = X10 ) )
& ( ( X5 = ordered_pair(esk3_2(X5,X8),esk4_2(X5,X8))
& X8 != esk4_2(X5,X8) )
| X8 = pair_second(X5) ) ) ),
inference(skolemize,[status(esa)],[33]) ).
fof(35,plain,
! [X5,X6,X7,X8,X9,X10] :
( ( ( X5 != ordered_pair(X9,X10)
| X8 = X10
| X8 != pair_second(X5) )
& ( ( X5 = ordered_pair(esk3_2(X5,X8),esk4_2(X5,X8))
& X8 != esk4_2(X5,X8) )
| X8 = pair_second(X5) ) )
| X5 != ordered_pair(X6,X7) ),
inference(shift_quantors,[status(thm)],[34]) ).
fof(36,plain,
! [X5,X6,X7,X8,X9,X10] :
( ( X5 != ordered_pair(X9,X10)
| X8 = X10
| X8 != pair_second(X5)
| X5 != ordered_pair(X6,X7) )
& ( X5 = ordered_pair(esk3_2(X5,X8),esk4_2(X5,X8))
| X8 = pair_second(X5)
| X5 != ordered_pair(X6,X7) )
& ( X8 != esk4_2(X5,X8)
| X8 = pair_second(X5)
| X5 != ordered_pair(X6,X7) ) ),
inference(distribute,[status(thm)],[35]) ).
cnf(39,plain,
( X4 = X5
| X1 != ordered_pair(X2,X3)
| X4 != pair_second(X1)
| X1 != ordered_pair(X6,X5) ),
inference(split_conjunct,[status(thm)],[36]) ).
fof(74,negated_conjecture,
? [X1,X2] :
( pair_first(ordered_pair(X1,X2)) != X1
| pair_second(ordered_pair(X1,X2)) != X2 ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(75,negated_conjecture,
? [X3,X4] :
( pair_first(ordered_pair(X3,X4)) != X3
| pair_second(ordered_pair(X3,X4)) != X4 ),
inference(variable_rename,[status(thm)],[74]) ).
fof(76,negated_conjecture,
( pair_first(ordered_pair(esk8_0,esk9_0)) != esk8_0
| pair_second(ordered_pair(esk8_0,esk9_0)) != esk9_0 ),
inference(skolemize,[status(esa)],[75]) ).
cnf(77,negated_conjecture,
( pair_second(ordered_pair(esk8_0,esk9_0)) != esk9_0
| pair_first(ordered_pair(esk8_0,esk9_0)) != esk8_0 ),
inference(split_conjunct,[status(thm)],[76]) ).
cnf(103,plain,
( pair_first(X1) = X2
| ordered_pair(X2,X3) != X1
| ordered_pair(X4,X5) != X1 ),
inference(er,[status(thm)],[31,theory(equality)]) ).
cnf(108,plain,
( pair_second(X1) = X2
| ordered_pair(X3,X2) != X1
| ordered_pair(X4,X5) != X1 ),
inference(er,[status(thm)],[39,theory(equality)]) ).
cnf(204,plain,
( pair_first(ordered_pair(X1,X2)) = X1
| ordered_pair(X3,X4) != ordered_pair(X1,X2) ),
inference(er,[status(thm)],[103,theory(equality)]) ).
cnf(211,plain,
( pair_second(ordered_pair(X1,X2)) = X2
| ordered_pair(X3,X4) != ordered_pair(X1,X2) ),
inference(er,[status(thm)],[108,theory(equality)]) ).
cnf(229,plain,
pair_first(ordered_pair(X1,X2)) = X1,
inference(er,[status(thm)],[204,theory(equality)]) ).
cnf(248,negated_conjecture,
( $false
| pair_second(ordered_pair(esk8_0,esk9_0)) != esk9_0 ),
inference(rw,[status(thm)],[77,229,theory(equality)]) ).
cnf(249,negated_conjecture,
pair_second(ordered_pair(esk8_0,esk9_0)) != esk9_0,
inference(cn,[status(thm)],[248,theory(equality)]) ).
cnf(373,plain,
pair_second(ordered_pair(X1,X2)) = X2,
inference(er,[status(thm)],[211,theory(equality)]) ).
cnf(400,negated_conjecture,
$false,
inference(rw,[status(thm)],[249,373,theory(equality)]) ).
cnf(401,negated_conjecture,
$false,
inference(cn,[status(thm)],[400,theory(equality)]) ).
cnf(402,negated_conjecture,
$false,
401,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU267+1.p
% --creating new selector for []
% -running prover on /tmp/tmpmnqcXM/sel_SEU267+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU267+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU267+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU267+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------